Determine whether each relation is a function, and state its domain and range.
Determine whether each relation is a function, and state its domain and range.
\displaystyle
3x^2 + 2y =6
Determine whether each relation is a function, and state its domain and range.
Determine whether each relation is a function, and state its domain and range.
\displaystyle
x = 2^y
A cell phone company charges a monthly fee of $30, plus $0.02 per minute of call time.
a) Write the monthly cost function, C(t)
, where t is the amount of time in minutes of call time during a month.
b) Find the domain and range of C
.
Graph f(x) = 2|x + 3| -1
, and state the domain and range.
Describe this interval using absolute value notation.
For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.
\displaystyle
f(x) =x^2
and \displaystyle
g(x) = \sin x
For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.
\displaystyle
f(x) =\frac{1}{x}
and \displaystyle
g(x) = x
For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.
\displaystyle
f(x) =x^2
and \displaystyle
g(x) = \sin x
For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.
\displaystyle
f(x) =2^x
and \displaystyle
g(x) = x
Identify the intervals of increase/decrease, the symmetry, and the domain and rage of each function.
\displaystyle
f(x) = 3x
Identify the intervals of increase/decrease, the symmetry, and the domain and range of each function.
\displaystyle
f(x) = x^2+ 2
For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.
\displaystyle
f(x) =|x + 1|
For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.
\displaystyle
f(x) = -0.25\sqrt{3(x+ 7)}
For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.
\displaystyle
f(x) = -2\sin(3x) + 1, 0 \leq x \leq 360^o
For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.
\displaystyle
f(x) = 2^{-2x} -3
The graph of y = x^2
is horizontally stretched by a factor of 2, reflected in the x—axis, and shifted 3 units down. Find the equation that results from the transformation, and graph it.
(2, 1)
is a point on the graph of y =f(x)
. Find the corresponding point on the graph of each of the following functions.
\displaystyle
y = -f(-x)+2
(2, 1)
is a point on the graph of y =f(x)
. Find the corresponding point on the graph of each of the following functions.
\displaystyle
y =f(-2(x+ 9)) - 7
(2, 1)
is a point on the graph of y =f(x)
. Find the corresponding point on the graph of each of the following functions.
\displaystyle
y =f(x -2) + 2
(2, 1)
is a point on the graph of y =f(x)
. Find the corresponding point on the graph of each of the following functions.
\displaystyle
y = 0.3f(5(x-3))
(2, 1)
is a point on the graph of y =f(x)
. Find the corresponding point on the graph of each of the following functions.
\displaystyle
y = 1 -f(1-x)
(2, 1)
is a point on the graph of y =f(x)
. Find the corresponding point on the graph of each of the following functions.
\displaystyle
y = -f(2(x - 8))
For the point on a function, state the corresponding point on the inverse relation.
(1, 2)
For the point on a function, state the corresponding point on the inverse relation.
(-1, -9)
For the point on a function, state the corresponding point on the inverse relation.
(0, 7)
For the point on a function, state the corresponding point on the inverse relation.
f(5) = 7
For the point on a function, state the corresponding point on the inverse relation.
g(0) = -3
For the point on a function, state the corresponding point on the inverse relation.
h(1) = 10
Given the domain and range of a function, state the domain and range of the inverse relation.
D = \{x\in \mathbb{R}\}
, \displaystyle
R = \{y \in \mathbb{R}, -2 < y < 2\}
Given the domain and range of a function, state the domain and range of the inverse relation.
D = \{x\in \mathbb{R}, x \geq 7\}
, \displaystyle
R = \{y \in \mathbb{R}, y < 12\}
Graph the function and its inverse relation on the same set of axes. Determine whether the inverse relation is a function.
f(x) = x^2 -4
Graph the function and its inverse relation on the same set of axes. Determine whether the inverse relation is a function.
f(x) = 2^x
Find the inverse of each function.
f(x) = 2x + 1
Find the inverse of each function.
f(x) = x^3
Graph the following function. Determine whether it is discontinuous and, if so, where. State the domain and the range of the function.
\displaystyle
f(x) =
\begin{cases}
&2x, &\text{when } x < 1 \\
&x +1, &\text{when } x \geq 1
\end{cases}
Write the algebraic representation for the following piecewise function, using function notation.
If
\displaystyle
f(x) =
\begin{cases}
&x^2 +1, &\text{when } x < 1 \\
&3x, &\text{when } x \geq 1
\end{cases}
is f(x)
continuous at x =1
? Explain.
A telephone company charges $30 a month and gives the customer 200 free call minutes. After the 200 min, the company charges $0.03 a minute.
a) Write the function using function notation.
b) Find the cost for talking 350 min in a month.
c) Find the cost for talking 180 min in a month.
Given f = \{(0, 6), (1, 3), (4, 7), (5, 8)\}
and g= \{(-1, 2), (1, 5), (2, 3) ,(4, 8), (8, 9)\}
, determine
f(x) + g(x)
Given f = \{(0, 6), (1, 3), (4, 7), (5, 8)\}
and g= \{(-1, 2), (1, 5), (2, 3) ,(4, 8), (8, 9)\}
, determine
f(x)- g(x)
Given f = \{(0, 6), (1, 3), (4, 7), (5, 8)\}
and g= \{(-1, 2), (1, 5), (2, 3) ,(4, 8), (8, 9)\}
, determine
f(x)\cdot g(x)
Given f(x) = 2x^2 -2x, -2 \leq x \leq 3
and g(x) = -4x, -3 \leq x \leq 5
, graph the following.
f
Given f(x) = 2x^2 -2x, -2 \leq x \leq 3
and g(x) = -4x, -3 \leq x \leq 5
, graph the following.
g
Given f(x) = 2x^2 -2x, -2 \leq x \leq 3
and g(x) = -4x, -3 \leq x \leq 5
, graph the following.
f +g
Given f(x) = 2x^2 -2x, -2 \leq x \leq 3
and g(x) = -4x, -3 \leq x \leq 5
, graph the following.
f -g
Given f(x) = 2x^2 -2x, -2 \leq x \leq 3
and g(x) = -4x, -3 \leq x \leq 5
, graph the following.
fg
f(x) = x^2 +2x
and g(x) = x + 1
. Match the answer with the operation.
\displaystyle
\begin{array}{llllllll}
&(a) \phantom{.} x^3 + 3x^2 + 2x
&A \phantom{.} f(x) + g(x) \\
&(b) \phantom{.} -x^2 -x + 1
&B \phantom{.} f(x) - g(x) \\
&(c) \phantom{.} x^2 +3x + 1
&C \phantom{.} g(x) - f(x) \\
&(d) \phantom{.} x^2 +x - 1
&D \phantom{.} g(x) \times f(x)
\end{array}
f(x) = x^3 +2x^2
and g(x) = -x + 6
.
a) Complete the table.
b) Use the table to graph f(x)
and g(x)
on the same axes.
c) Graph (f 1 g)(x) on the same axes as part b).
d) State the equation of (f + g)(x)
.
e) Verify the equation of (f + g)(x)
using two of the ordered pairs in the table.